Algebra Archive: Questions from April 28, 2023
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\( \left[\begin{array}{lll}0 & y & 1\end{array}\right]\left[\begin{array}{ccc}-1 & 1 & 2 \\ 0 & 3 & 1 \\ -1 & 5 & 1\end{array}\right]\left[\begin{array}{l}y \\ 1 \\ 2\end{array}\right]=3 \)2 answers -
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\( \begin{array}{l}y^{3}+3 x y^{2} z-2 y z=0 \\ z=\frac{1}{3 x} \\ z=\frac{-y^{3}}{3 x y^{2}-2 y} \\ z=\frac{-y}{3 x-2 y} \\ z=\frac{-y^{2}-2}{3 x y}\end{array} \)2 answers -
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5. Diagonalize the matrix \( \left[\begin{array}{rr}1 & 0 \\ 6 & -1\end{array}\right] \), if possible.2 answers -
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Select all first partial derivatives of \( 2 x^{2} y-6 x \sqrt{4 y} \) a) \( 4 x-\frac{6}{\sqrt{y}} \) b) \( 4 x y-\frac{12 x}{\sqrt{y}} \) c) \( 4 x y-12 \sqrt{y} \) d) \( 3 x^{2}-\frac{6 x}{\sqrt{y}2 answers